330

23

Regulatory Networks

at a later epoch tt; hence (cf. Eq. 23.11),

nu left parenthesis t right parenthesis equals integral Subscript 0 Superscript t Baseline k Subscript normal a Baseline left parenthesis t 1 right parenthesis c Subscript normal upper A Baseline left parenthesis t 1 right parenthesis phi left parenthesis t 1 right parenthesis upper Q left parenthesis t comma t 1 right parenthesis normal d t 1 periodν(t) =

{ t

0

ka(t1)cA(t1)φ(t1)Q(t, t1) dt1 .

(23.21)

The memory function, as well as all the other parameters in Eq. (23.21), can be

determined from the high-resolution association and dissociation kinetics.

Further advantages of the biosensor approach include the ability to study collective

and coöperative effects and to determine the precise stoichiometry of the association.

23.8.3

Protein Chips

In order to enable many interactions to be measured simultaneously, microarrays

have been developed. ³³ With these arrays, the interaction of protein A with thousands

of other proteins can be studied in a single experiment, by letting A flow over the array.

Some kind of marking of A (e.g., post-reaction staining) is typically required to allow

the identification of its presence at certain sites on the array. The physical chemistry

of operation of these devices is governed by the same basic set of equations as for

the biosensor approach (Sect. 23.8), although it is not presently possible to achieve

the same sensitivity and time resolution. ³⁴

23.9 Interactions from Sequence

The principle of this approach is that gene proximity is the result of selective evolu-

tionary pressure to associate genes that are co-regulated and, hence, possibly interact-

ing. The motivation is to develop a method that is far less tedious and labour-intensive

(and hence expensive) than the experimental techniques discussed in the preceding

two sections, yet no less accurate.

Certain proteins (in a single given species) apparently consist of fused domains

corresponding to individual proteins (called component proteins) in other species.

The premiss of the method is that if a composite (fused or fusion) protein in one

species is uniquely similar to two component proteins in another species, which may

not necessarily be encoded by adjacent genes, those component proteins are likely

to interact. “Interaction” may be either physical association or indirect functional

association such as involvement in the same biochemical pathway, or co-regulation.

Hence, what is inferred from this method does not exactly correspond with what is

measured in the experimental methods. Nevertheless, it is an interesting attempt and

33 See Sect. 18.5; the immobilization of proteins without altering their conformation, and hence

association characteristics, is however more difficult than for nucleic acid oligomers.

34 See also Sect. 18.1 for limitations of the technique.